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Investigations in music similarity: analysis, organization, and visualization using tonal features

INVESTIGATIONS IN MUSIC SIMILARITY:
ANALYSIS, ORGANIZATION, AND VISUALIZATION USING TONAL
FEATURES
by
Arpi Mardirossian
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)
August 2007
Copyright 2007 Arpi Mardirossian

This dissertation is in the area of music information retrieval, which is an interdisciplinary science that incorporates knowledge and expertise from artificial intelligence, music theory, mathematical modeling, computational analysis, databases, music perception and music cognition. We are focused on developing computational ways to accurately assess, quantify, and visualize degrees of musical similarity. This involves the end-to-end development of computational tools, from the design of the mathematical models, to the implementation and testing of the algorithms on large datasets, to the creation of an intuitive and user-centered interface for communicating the results. This dissertation has two parts: music similarity assessment and music visualization.; Music similarity assessment is a complex problem; definitions of similarity can diverge widely and be highly subjective. Can we build computer models to recognize these different degrees of similarity? Our work addresses this question, and has focused on the development of similarity metrics based on tonal features, which are obtained from pitch and key information. We have developed four methods of similarity assessment, each using one of the following features: pitch class distributions, key sequences, key distributions, and mean-time-in-key distributions, and based on one of the following similarity metrics: L1 norm, L2 norm, and sequence alignment.; We use the similarity assessment techniques to conduct two sets of experiments: the first uses different renditions of pieces, while the second uses theme and variation pieces. For each experiment, all four methods are used to compare the pieces in each data set one to another. Statistical analyses such as quantile-quantile plots and the Kolmogorov-Smirnov test confirm that comparison results from within similar and across dissimilar sets come from different underlying distributions for all the methods. A Mann-Whitney rank sum test confirms that results for similarand dissimilar pieces come from distributions with different medians for all the methods. We further compute Type I, Type II and Bayesian probabilities to analyze each method's performance.; While metrics are a quick and clear way to determine similarity, visualizations can add a richness and complexity to the analysis. Our goal is to present music information in a visual form that is intuitive and easy to access. One method of visualization we have developed is a dynamic visualization that displays the progression of the tonal content of a music piece on a two-dimensional representation of keys. The sequence of keys in a music piece is mapped onto a space that contains points representing all possible keys. The distribution of keys of a piece being visualized is indicated as growing colored discs, where the colors correspond to the keys detected, and the size of the discs to the key frequency. This visualization is an improvement over more basic charting methods, such as histograms, and it maintains standards of information design in the form of added dimensionality, color, and animation. We show that the visualization is invariant under music transformations that preserve the piece's identity.; We demonstrate the dynamic visualization system using two music genres. We consider classical and Armenian music. Classical music tends to follow a pattern of beginning in the key of the piece, traveling to neighboring keys throughout the course of the piece before returning to the key of the piece in the end. In contrast, Armenian music follows a more sequential pattern where the piece begins in a key, remains there for a period of time before moving on to other keys. It rarely ends in the key it first visited. We use the visualization method to illustrate these patterns for a set of classical and Armenian pieces.; Another method of visualization we have developed exploits the tonal properties of music to derive a hierarchical description for each piece that can then be used in conjunction with the dynamic visualization. The visualization is generated using a tree of keys in circular formation. This static aggregate visualization is a high-level, 'aerial' version of the dynamic visualization that allows a user to get a quick-glance overview of the dynamic visualization of a piece. We illustrate the usefulness of this visualization through several examples.

INVESTIGATIONS IN MUSIC SIMILARITY:
ANALYSIS, ORGANIZATION, AND VISUALIZATION USING TONAL
FEATURES
by
Arpi Mardirossian
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)
August 2007
Copyright 2007 Arpi Mardirossian